A
group of researchers are designing an experiment to test the IQ of a
monkey. They will hang a banana at the roof of a building, and at the
mean time, provide the monkey with some blocks. If the monkey is clever
enough, it shall be able to reach the banana by placing one block on the
top another to build a tower and climb up to get its favorite food.
The
researchers have n types of blocks, and an unlimited supply of blocks
of each type. Each type-i block was a rectangular solid with linear
dimensions (xi, yi, zi). A block could be reoriented so that any two of
its three dimensions determined the dimensions of the base and the other
dimension was the height.
They want to make sure that the
tallest tower possible by stacking blocks can reach the roof. The
problem is that, in building a tower, one block could only be placed on
top of another block as long as the two base dimensions of the upper
block were both strictly smaller than the corresponding base dimensions
of the lower block because there has to be some space for the monkey to
step on. This meant, for example, that blocks oriented to have
equal-sized bases couldn‘t be stacked.
Your job is to write a program that determines the height of the tallest tower the monkey can build with a given set of blocks.
The input file will contain one or more test cases. The first line of each test case contains an integer n,
representing the number of different blocks in the following data set. The maximum value for n is 30.
Each of the next n lines contains three integers representing the values xi, yi and zi.
Input is terminated by a value of zero (0) for n.
For
each test case, print one line containing the case number (they are
numbered sequentially starting from 1) and the height of the tallest
possible tower in the format "Case case: maximum height = height".
1
10 20 30
2
6 8 10
5 5 5
7
1 1 1
2 2 2
3 3 3
4 4 4
5 5 5
6 6 6
7 7 7
5
31 41 59
26 53 58
97 93 23
84 62 64
33 83 27
0
Case 1: maximum height = 40
Case 2: maximum height = 21
Case 3: maximum height = 28
Case 4: maximum height = 342
#include <iostream>
#include <memory.h>
#include <string>
#include <istream>
#include <sstream>
#include <vector>
#include <stack>
#include <algorithm>
#include <map>
#include <queue>
#include <math.h>
#include <cstdio>
#include <set>
#define ME(x , y) memset(x , y , sizeof(x))
#define SF(n) scanf("%d" , &n)
#define rep(i , n) for(int i = 0 ; i < n ; i ++)
#define INF 0x3f3f3f3f
#define mod 998244353
#define PI acos(-1)
using namespace std;
typedef long long LL;
int dp[189];
struct node
{
int x , y , z ;
}a[189];
bool cmp(struct node a , struct node b)
{
if(a.x < b.x)
{
return 1 ;
}
else if(a.x == b.x)
{
return a.y < b.y ;
}
else return 0;
}
int main()
{
int n ;
int cnt = 0 ;
while(~scanf("%d" , &n) && n)
{
int l = 0 ;
for(int i = 0 ; i < n ; i++)
{
int x , y , z ;
scanf("%d%d%d" , &x , &y , &z);
a[l].x = x , a[l].y = y , a[l++].z = z ;
a[l].x = x , a[l].y = z , a[l++].z = y ;
a[l].x = y , a[l].y = x , a[l++].z = z ;
a[l].x = y , a[l].y = z , a[l++].z = x ;
a[l].x = z , a[l].y = x , a[l++].z = y ;
a[l].x = z , a[l].y = y , a[l++].z = x ;
}
sort(a , a+l , cmp);
/*for(int i = 0 ; i < l ; i++)
{
cout << a[i].x << " " << a[i].y << " " << a[i].z << endl ;
}*/
for(int i = 0 ; i < l ; i++)
{
dp[i] = a[i].z ;
for(int j = 0 ; j < i ; j++)
{
if(a[j].x < a[i].x && a[j].y < a[i].y)
{
dp[i] = max(dp[i] , dp[j]+a[i].z);
}
}
}
int ans = -INF ;
for(int i = 0 ; i < l ; i++)
{
ans = max(ans , dp[i]);
}
cout << "Case " << ++cnt << ": maximum height = " << ans << endl;
}
return 0;
}
